Method and machine foe mechanically obtaining the pboduct of numbers



June 6, 1933. H. PKNKEL ET AL 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet l ATTORNEY.

H. PINKEL ET AL June 6, 1933.

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet 2 g M INVENTORS. v

33/7 277a P/n/fc/ 0m n amm P/mrcl ATTORNE-Y.

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METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet 3 ATTORNEY.

June 6, 1933. H. PlNKEL ET AL 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS 1928 14 Sheets-Sheet 4 Filed Ogt. so,

INVENTORS man P/n Ad and mzzmm Witness A TTORNE Y.

June 6, 1933. H. PINKNEL ET AL 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet 5 B INVENTORS. gman Pin/{cl nd 14 Sheets-Sheet 6 INVENTIORS ma )7 P; n jamm ATTORNEY.

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METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 50, 1928 14 Sheets-Sheet 7 June 6, 1933.

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS H. PINKEL Er AL 1,912,857

Filed Oct. 30, 1928 I36 /a 9 KIM ,37 53 //z IE 5 I/wpv ram Hy man Pm/ie/ @1 4 June 6, 1933. H. PINKEL E1 AL 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet l0 0 n J W .H hP M ME. 0 I W 7 mmm H m W I o w 5 =iV///// S m 0 a3 w 5 W0 A 5 v x 6 n w W June 6, 1933. H. PINKEL ET AL. 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet ll INVENTORS fzQ mafia'mfq/ n Benjam/n Pm/rd.

June 6, 1933. H. PINKEL ET AL METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed 001;. 30, 1928 14 Sheets-Sheet l2 B n/arm); 7m/f l ATTOIIZNEY.

a C .M l W J 1933- H. PINKEL ET AL 1,912,857

METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Wrmss ATTORNEY June 6, 1933. H, PINKEL ET AL METHOD AND MACHINE FOR MECHANICALLY OBTAINING THE PRODUCT OF NUMBERS Filed Oct. 30, 1928 14 Sheets-Sheet l4 iNVENToR s 9 ma 7 Fu rk am/ B njam/n Pm/re/ TTO f/VEY W/fness Patented June 6, 1933 HYMAN PINKEL AND BENJAMIN PINKEL; OFl PfIIL ADELPHIA, PENNSYLVANIA METHOD AND MACHINE FOR MEcHANIoALLYoB'rAmiiiG THE PRODUCT F NUMBERS Application filed October 30, 192 8 erial No. 316,010;

Our invention relates to methods and means formechanically obtaining the products of numbers. 1

We are aware that various adding and Table I :"calculating machines have been heretofore produced but, to the best of our knowledge, I 1 1 (D) (0) an all suchmachines require considerable manipulation in order to obtain the product of two numbers such as the impression of one an M factor and then subsequently each digit'of a c0 the other factors with the clearing of the machine for each digit of said second factor. Among the objects of our invention are to provide amethod of mechanically obtaining the product of two numbers and a machine adapted for carrying out the method, and to provide such a machine susceptible of use with a single ordinary keyboard upon which the factors may be successively impressed by impressing all of the digits of each factor V I and the product thereof obtained by a single manipulation of an operating control.

The basis of our method is the formula that the product of two numbers is equal to c h 9,, one-quarter of the square of the sum of the 4 4 two numbers minus one-quarter of the square -9 We have of the difference between the two numbers, Table H and an object of the invention is to provide a. method and a machine which calculation (F) (E) (D) (C) (B) (A) may be made on this basis.

l By the use of this formula, which can be a b a used in various forms, we are allowed to f a h bring the multiplier and multiplicand to- @%J 5:2 gether on certain mechanism in the form of a -(bh) wi h their sum and difference and obtain the prodi 4 not of the two numbers by obtaining the 4 4 4 quarter-squares of the sum and difference and then finding the difference between the i-Q w)? 1) quarter-squares thus produced. {f z L M to In multiplying two numbers, the intergers T T T of the multiplicand' are individually and successively multiplied by the integers of the is multiplied by a number represented by fgh, the individual products of the integers are arran ed in columns in the usual manner, as shown in'the following table.

As previously stated, the product of two numbers is equal to the difference between the quarter-squares of their sum and difier- 60 ence or, expressed algebraically,

If the sum of two numbers is even, the difmultipier. If a number represented by abcference Will {L180 even nd' e 'quartersquares of the sum and the difference will be whole numbers but, if their sum is odd, their 90 Byconverting the individual products in the several columns of Table I into their algebraic equivalents, that is difference will be odd and the quartersquares of their sum and difference will each contain a fraction. As the quarter-square of the difference is subtracted from the quartersquare of the sum, the fractions, if any, cancel each other and have been disregarded in the construction of the machine.

As one-half of the quantities are negative, they may be subtracted directly from the positive quantities or the complements of the negative quantities used. In the latter case,

the complements of the negative quantities are added to thepositiye quantities and'cei' tain vaules arbitrarily placed in certain columns to cancel the base figures employedin obtaining the complements; thatis,'i if 100 is used as the base and one complement falls in the right hand column, a valueof nine is placed in the third column which, added to the one carried over from the 100,

equals ten, transfers a one to the next colunm,

and leaves the third column unafi'ected by .the base figure used in the first column.

We have found that several types of machines may be produced for carrying our invention into effect. For the purpose of illustration, we have shownand described a machine employing the formula given in the following table and in which the complements are substituted for negative quantities but we do not limit ourselves to the particular phase of the formula employed or to the specific machine illustrated and described.

The following table is the same as Table II except that the quantities in each column have been rearranged to conform to the positions of certain mechanisms in the machine presently to be described, the negative quantities replaced by their complements, and certain figures arbitrarily added into certain columns for canceling the base figures used.

When the amounts in each column are distributed, the base figure (100) added to column A will cause a 1 to fall in column C which, added to the 9 arbitrarily placed therein, equals 10 and causes a 1 to fall in column D. The two base figures added to column B will cause a 2 to fall in column D which, added to the 7 arbitrarily placed therein and to the 1 carried over from column C, equals 10 and causes a 1 to fall in column E. The three base figures added to column C cause a 3 to fall in column E which, added to the 6 arbitrarily placed therein and to the 1 carried over from column D, equals 10 and causes a 1 to fall in column F. The two base figures added to column D cause a 2 to fall in column F which, added to the 7 arbitrarily placed therein and to the 1 carried over from column E, causesa 1 to fall into the next column, if any, or out of the table or machine if but six columns or decimal places are employed. The base figure placed in column E will cause a1 to-fall in the column to the left of column F, if any, or out of the table or machine if but six'columns'or decimal places are employed.

As the values of the integers impressed upon the machine range from 0;to 9, the sum oftwo integers (art-y) will range-from 0 to 18, the quarter-squares of the sums range from O to- 8 1,- the differences between two integers range from 0 to'9, and

the complements of the quarter-squares of thedifferences V range from 80 to In Tables and III, the product of thetwo integers is shown in each column. In themachine, the .value. of the units figure ofa product in any one The units parts of theamounts shown in the several columns of Table III are indicated by (U) and shown in corresponding columns in Table IV, which is shown on the drawings as Figure 28, and the ten parts of those amounts shown in the next higher column and indicated by (T). The arbitrary figures added into the columns of Table III are omitted from Table IV as they are taken care of in the registering mechanism as will presently be described.

Both the 'units and tens parts of the various amounts are shown in boxes which represent converting units having a gear forming a part of each. The gear of each converting unit is indicated by its reference numeral and shows the integers which are transfixed to it by the distributing mechanism and whether the second integer is added to or subtracted from the first integer. Before describing the method further, mechanism for carrying it into effect will be described. .I

A machine embodying our invention consists of tabulating mechanism upon which the numbers to be multiplied are impressed, ove'r mechanism, certain parts ofwhichare distributing mechanism-which"arrangesithe broken away. Y sums and differences of the several integers Figure 8 *is a detail view showing the stopof the numbers to be multiplied, converting ping disks and the means for holding themmechanism which receives the sums anddifagainst rotation; the view being taken in the fercnces from the distributing mechanism'and plane ofline 8- 8 on Figure 1. r converts the sums into their quarter-squares Figure 9 is a transverse section taken on and the dilierences into the complements of line'9 9 on Figure 1, their quarter-squares in accordance with Figure 10 a fragmentary transverse section- Table III, all of whichis divided into banks" taken on the broken line 1010 on Figure 2, f corresponding to the columns in Tables I to and I11, registering mechanism having means Figure 11 a transverse section showing the, for causing an upper bank to register for racks which drive the distributing-mechw; every time the. nextlower bank has registered nism, the springs and gears which drive'the ten times and havingdials upon which the": converting mechanism and the-mechanism final product is registe'red, and driving meek-* for clearing thetabulating'mechanism; the anism'i'or actuating the other mechanisms; view being taken in the plane of line 1111 1 For the sake of simplicity, tables have been on Figure 1. 1 Y I given for three-place numbers only and a ma- Figure 12 is a fragmentary transverse secchine having but three banks of key's'and-six tion, taken on line 1212 on Figure 1, show-' banks of mechanisms illustrated in the accom- 1 ing-the gearing which connects the several panying drawings as a: machine of greater banks of converting mechanism; 1 capacity may be produced-by duplication of" Figure l3'adetail view, taken substantial parts. Adding and subtracting mechanisms ly on'line i3-13 on Figure l',-showing oer-"- havenot been shown as these functions are tain details of thedrivingi inechanismy well. known and it wouldme'rely lie-necessary Figure 14 a detail view, taken-in the plane to disconnectthe distributing and converting 'of-;.line. I l-14 ion Figure 1', showing -mchamechanisms and connectthe tabulating mechnism. for driving the tabulating mechanism anism directly to the-registering inechanisin and ',-Lv Y I to produce these functions. Figures 15 and 16, respectively, an eleva Referring to the drawings, in which sevtion and a central section ofan arm forming oral ofthe' views show the parts which are in a partoi the converting mechanism. the immediate foreground 'only'as the inclu- Figures 17, 19,21, 22 and 24: are detail sfon' of the parts in the back ground would views of gears forming parts. of the conrender-these views soeomplicated that they vex-ting mechanism, and u would be unintelligible,' l l Figures 18, 20, 23 and 25 detail Views" of Figure- 1 is a longitudinal elevation of a ship-plates forming parts of the converting machinein which our invention is embodied m'echanismi with the'side'ot the casing removed; Figure 26 is a schematic sectional plan Figure 2v a longitudinal section; taken 1 view of'the distributing mechanism shown in through the center of the'second bank of Figure 5 but drawn to a largerscale andzwith mechanism as indicated by line 2-2011 Figcertain parts broken awayand other parts 9 d v omitted. w a

Figure 3 a longitudinal section taken on Figure 27 is a view similar to Figure 26 but lin 3 -3 n Figur 9, with the parts shown in different positions. Fi 4 i a ti l l i t k Figure 28 IS a diagram showing, schematisu'bstantially on line 4-4; on Figure 1, show- 3 3", the g of the q r g lnecha' ing only the driving mechanism, the upper w i the distnbutmg mech banks of the converting mechanism and the Wnch i them and also q 1 upper banks of the registering mechanism. fi i i l z W 5 each f f' Figure 5 is a sectional plan view, taken subf t T i 2 stantially on the broken line 5 5 on Figure 1, 81 Squaw O amoun 01 1 S comp? z f t g i dlstmlbutlng l fi j 9. As the banks of mechanisms correspond to m 5 i mmsm 1e uvnlg the columns in Tables Ito III they have-been mechanism in central section, and certain g designated A, B, C, D, E and F to correspond P ri of the F l with the similarly designated columns in the 6 1S a fsectlonal 1 "716W, taken tables. In order that the elements of one Substantially on 11119 6'5 on g Show part of the machine may be readily distining only thelower banks of the'converting i h d f thOse of other parts of the mechanism, thelOWeI' banks of the registev machine,refercnce numerals under 100 have ing mechanism and sectionsof certain parts b li d t th casing t n l b of the driving mechanism. tween 100 and 199 to the tabulating mecha- Figure 7 is a transverse section, taken on nism, numerals between 200 and 399 to the line.7'7 on Figure 1, showing the carryingconverting mechanism, numerals between 400 330 and, 599 to the distributing mechanism, numerals between 600 and 699 to the registeringmechanism, and numerals between 700 and 799 to the driving mechanism.

Referringnow more particularly to Figuresl, 2 and 9, the-mechanisms are mounted in a casing 51 having key guides 101 arranged in three rows of nine each in its upper wall. Slidably mounted in each row of guides are keys 102 which-differ only in the lengths of their shanks and in the figures displayed upon their tops. The keys are held in their upper positions by springs 111 which may be tension springs and have one end of each secured .to a key guide or the wall of the easingvandthe other end to the shank of the key.

Struts 52 and 53 extend transversely of the casing. and slidably support three keybars 112, each of which is mounted adjacent a row.of keys and has nine pins or projections 113 extending from one side and abutting the-sloping faces 114 on enlargements 104 formed. near the lower ends of the keys ad having stops 115 on their upper edges. In order to hold each key in alignment when it is depressedto force face 114 across pin 113, aprojection' or pin 116 is formed onor secured in its lower end and slidably mounted in a guideway 117 formed on a guide bar 118 supported between struts 52 and 53. Each keybar is non-rotatable and held in its operative position, as shown in Figures 1 and 2, by a coil spring 119 encircling its rear end and abutting strut 53.

Beneath each bank of keys, a shaft 120 is rotatably. mounted in struts 52 and 53 and in a bearing 121 secured to the rear wall of the casing. Spaced progressively one-tenth of a revolution apart around the shaft and rigidly secured thereto are ten arms 122 and 123, the nine arms 123 being in alignment with the nine keys and the arm 122 in align ment with and normally abutting an arm 124 fixed on keybar 112. Arm 122 represents the zero position and holds shaft 120 against rotation unless one of the keys is depressed, causing the face 114 on that key to move along the pin 113 with which it is in contact and move keybar 112 against the action of spring 119 sufficiently for arm 124 to clear arm 122.

Shaft 120 may then rotate until the arm beneath the depressed key comes in contact with the lower end of that key. When the key is fully depressed, spring 119 will draw the keybar rearwardly and cause the pin 113, which is in contact with that key, to ride onto the top of enlargement 104 and against stop 115, thus holding the key against upward movement and the keybar from returning suffic ently to bring arm 124 in alignment with arm 122. \Vhen arm 124 is in contact with arm 122, shaft 120 is held against rotation; whenthe number one key is depressed, shaft 120 may make one-tenth of a revolution; when the number two key is depressed, the .shaftmay make two-tenths of a revolution, etc. 1 a

A sprocket gear 126 is ,rotatably mounted on each shaft 120 and driven by a chain 127 which isactuated by a sprocket gear 128 fixed for rotation with a bevel gear 129 and rotatably mounted in a bracket bearing 130 secured to the side wall of the casing (see also Figures 3 and 14). A bevel gear 131 is rotatably mounted on a stub shaft 132 on hearing 130 and meshes withbevel gear 129. A spur gear 133, also mounted on shaft 132, is fixed for rotation with gear 131, and meshes with a segmentalfgear 750 forming apart of the driving mechanism.

Sprocket gears 126 are each connected to a shaft 120 by means of a spiral spring 134 which hasone end secured to the gear and the other end=.to the shaft. ,When a key isdepressed'and segmental gear 750 is actuated, gears 133,131,- ,129, and l28 will be rotated, chain 127 driven and gears 126 rotated, thus rotatingeach shaft 120 through the connection of spring .134- until an arm 123 abuts the end of the depressedkey, after which spring 134 permits gear:126 to complete its revolution. I

A shaft 135, rockably mounted in bearings 136 and 137 fixed to the side walls of the easing, has an arm 138 abutting the end of each keybar 112 for forcing the same forwardly against the action of spring 119 in order to move pins 113 clear of enlargements 104 and allowvany'key that may be depressed to be returned by its spring 111 (see also Figure 11). A lever 139 has one end fixed on shaft and its other end hinged to a lever 140 mounted intermediate its ends on a stub shaft 141 formed on a bearing 142 which is fixed to the side wall of the casing. When the dis trib-uting mechanism is shifted, as will be presently described, it engages the lower end of lever 140 and swings it, causing lever 139 and shaft 135 to be rocked, keybars 112 forced forwardly, and the keys released.

Rotation of each shaft 120 is transferred to the distributing mechanism through a gear 143 fixed on the shaft and meshing with a rack 144 which has its upper end slidably mounted in a guide 145 and its lower end in mesh with a gear 401 which forms a part of the distributing mechanism.

Referring now also to the other views, the principal parts of the converting and recording mechanisms are mounted upon six shafts indicated by reference numerals 201, 202, 203, 204, 205 and 206 which correspond to columns A, B, C, D, E and F, respectively, in Tables I to III. The shafts are arranged in two tiers and rotatably mounted in bearings 207 secured to the end walls of the casing; shafts 201, 203 and 205, which are shownin Figure 1 fransrersely of the casingand supports these shafts between the converting and recording mechanisms. Struts 56 and 57 extend transversely of the casing below struts 5 1 and 55,

respectively, and similarly support shafts 202, 204 and 206.

A sleeve 208, rotatably mountedlupon the rear end'of shaft 201, has abevel: gear 209 fixed on one end and meshing with a bevel gear 2l0 fixed on one end of a shaft 211 rotatably mountedina bearing 212-and having .a sprocket; gear 213 fixed on itsother endand engagedby a'- chain: 7 11 forming 1a part of the driving mechanism. A gear 214 is fixed on the other end .of sleeve 208 andsimilar gears 215are rotatably mounted upon the .rear ends-0f shafts 202 to 206 inclusive.:. 1.

A hearing .216 is'1nounted on the rear wall of the casing between shafts 201and 203 and rotatably supports an idler .gear 2 17-which meshes with gear 21a and witlivthe. gear 215 on shaft 203.v Similar bearings 216- are mounted between shaftsg203 and 205, 202'and 204, and 2,01 and, 206. and rotatably. support. idler gears 217. which unesh withthe gears nism is actuated to rotate sprocket wheel 213,

gears 21 1-and'215 will be rotated equally.

An arm 220 is secured to each .of gears 21 1 and 215 and has one end of a spiral spring 221 secured to its outer end, the'other end of the spring being secured'to the shaft upon which the gear is mounted, as best shown in Figure 11. When gears 21 1 and 215 are-rotated, springs 221 will be wound up and rotate the shafts until they are stopped by certain parts of the converting mechanism as will presently be described.

The converting mechanism on each ofthe shafts consists of from two to ten converting units and each unit consists of a gear, an arm and a stop plate. The; arms, shown in detail in Figures 15 and 16 and marked 8, are all alike except for the manner in which they are mounted upon the shafts and sleeves, as shown in Figures 17 to There are five kinds of gears and four kinds of stop plates; the different kinds of gears being lettered a, I), 0, (Z and e and the different kinds of stop plates 5/, 7L, 7: and m, respectively. In-ord'er to clearly explain the functions of'themachine, each arm, gear and stop plate hasbeen given a separate reference numeral to which has been added the letterindicating its kind as an exponent. For example, gears 231 and 328 are alike but are mounted in different locationsand adapted to .receive different combinations-of integers. In order that the stop plates may be mounted upon the shafts, each is secured to a disk 222 and, as the stop plates are sometimes adjacent one another and sometimes spaced apart, a disk 222 may have a stop plate on either side or upon both sides. Shafts 201 to 206 have sleeves. rotatably "mounted upon them and, in each converting un t, the gear is rotatably mounted while either the arm or the stop plate may be fixed for rotation with a shaft or a sleeve. The arms and-stop plates coact to stop rotation of the shaft, therefore, either the arm or the "stop plate may be'consi'dered as a stopping element. Theforwardmost stopping element on each shaft is fixedifor rotation with a sleeve. which is connected'to the registering mechanism; the rearmost stopping element on each shaft is fixed: for rotation with the shaft; the stopping element next to' the rearmost stopping element is hired for rotation with the followingstopping element; the 'nextstopping element, if; any, is fixed f0I I0i3at1Ol1iW1f/l1 the followingstopping element, and succeeding stoppingzelements, ifany, are similarly arranged. f -The stopping elements, which are fixed-for rotation with each other, are both fixed ,tojthe same sleevewhich is rotatable on :theshaft'. 3 The short sleeves, which connect -.two:=stopping elements,'have not been describedas this method of connecting two parts one shaft is well known. A typical arrangement isfshown inFigure 2 in which a the second bank of converting mechanism is shown' in central section.

In the first bank of converting mechanism, shaft 201 has a gear 223 rotatably mounted uponit and spaced from sleeve 208'by a sleeve "22 1. An arm 225 is fixed to the shaft between gear 223' and a-s'top plate 226 secured to a disk 222 which is fixed on one end of a sleeve 227 rotatably mounted upon the shaft. A second disk 222 is fixed on the other end of sleeve 227 and carries a stop plate 228 which coacts with an arm 229 fixed on the rear end of a sleeve 230 whose forward end is secured to a part of the registering mecha nism. A gear 231*, rotatably mounted on SlGCXG 230, coacts with arm 229 and is held in nism, a disk 222 isfixed to shaft 202, spaced from strut 56 by a sleeve 232, carries a stop a 'gear 256*; arm 255 being fixed for rotation with sleeve 234'and the stop plate being fixed to disks'222. I

In the third bank of converting mechanisn1,'a gear 257 is rotatably mounted upon shaft 203 and'fol'lowed by an .arm=2.58 which fixed to the shaft and followed successively .by-a stop plate 259", a stopplate 260 ,-.an arm 261 a gear 262, a gear 263-,- .an arm part 350 adapted to-be fixed for rotation with a shaft or a sleeve, as by inserting a key'in the keyway 351. A guideway 352 extends inwardly from one end and has a tongue 353 extending the entire length of each of its sides. VA slider 354 is mounted in the guideway and provided with grooves in its edges for receiving tongues 353 so that it is free .to slide longitudinally of the guideway but is=held-against movement transversely there of. :A pin 358 is fixed in the slide and extends 264 a stop plate 265*,a stop plate 266,=an

arm 267 a gear 268, a gear 269, an arm 270 astop plate 271, a stop plate 272, an J arm 273 a gear 274, a gear 275,- an :arm

276 a stop plate 277 a stop plate 278", an

arm 279, a gear 280, a gear 281, an arm 282,

at stop plate 283, a stop plate 284 ,an arm 285 ,and a-gear 286; arm 285 being fixed to sleeve 235 and gear 286 being'irotatable upon the sleeve and abutting strut 55w shaft 204 and followed by'an arm 288. which is 'fixed'to the shaft and followed vsuccessive- 1 1y by a stop plate 289, 'astop plate 290 an arm 291:, a gear 292, a gear 2934,":1narm 294 a stop plate 295 a stop plate 296, an

arm 297 agear' 298*, a gear 299,'an arm 300, a stop plate 301, a stop plate 302*, an

3111T3O35, a gear 304, a gear 305, an arm 306,-a stop plate 3075a stop plate 308, an

' arm 309, a gear 310, a gear311, an arm 312,

' ing rotatable upon a stop plate 313", a stop 'plate 314, an arm from each of its sides so that one of its ends may slide in a cam groove in a converting :gearand the other engage the stops on the stop plates. A leaf spring 356 has one endsecured to the side of the arm and the other endscurved" to approximately the radius of the converting gears and provided "with a promotion or offset-357 for engaging the teeth of the gear with which the arm to which"- it is securedis associated. The leaf spring tends to prevent movement of the converting gear, relatively to the arm, when the gear is not being driven by a gear in the distributing mechanism or the'arm being swung during-" the clearing and resetting processes.

In the fourth bank of converting. mechanism, a gear .287 is rotatably mounted upon 5 The converting gears shown on Sheet 11 of the drawings are all alike'except for the cam'g'roove formed in one'face of each. Gear a.,-sho'wn in Figure 24, is adapted to re- 4 ceive the "sum of two integers (w+y) and to coact with stop plate g, shown in Figure 25, for producing the units part of the quarter-square of that sum Gear b, shown in Figure 19, isadapted to receive the same sum as gear a and to coactwithfstop plate h, shown in Figure 20, for

producing the tens part of the quarter-square of that sum.

this gear and followed successively by a stop I plate 319", a stop plate 320, an arm 321, a gear 322, a gear 323, an arm 324, a stop plate 325, a stop plate 326 an arm 327 a gear 328, a stop plate 329, an arm 330, a

gear 331, a gear 332, an arm 333* and a stop plate 334 which is fixed for rotation with sleeve 237.

In the sixth bank of converting mechanism, a gear 335 is rotatably mounted upon shaft 206, an arm 336 fixed to the shaft adjacent the gear and successively followed by a sto p plate 337", a stop plate 338", an arm 339 and a gear 340; ear 340 being rotatable on sleeve 238 and arm 329 being fixed for rotation with the sleeve.

' Referring now more particularly to Figures 15 and 16, the arm 8 consists of a body Gear d, shown in Figure 22, is adapted to receive the difference between two integers (av-y) and to coact with stop plate m, shown in Figure 23, for producing the units part of the complement of that difference. Gear 0, shown in Figure 17, is adapted to receive the same amount as gear d and to coact with stop plate is, as shown in Figure 19, for producing the tens part of that complement.

Gears a c and d have cam grooves which are symmetrical about their vertical diameters, relatively to the positions shown in the drawings, and can be faced in either direction upon a shaft, but gear (2 has a cam groove which renders it unsymmetrical so that it-can be faced in but one direction on a shaft, consequently, gear e, which is exactly opposite hand to gear 6, and shown in Figure 21 is provided.

Before describing the gears and stop plates l 

